OAKLAND — One month after Jahi McMath entered Children’s Hospital Oakland for surgery to treat sleep apnea — and just days after she was taken out of the facility after a fierce legal battle — her family says the teenager’s health is improving as she receives nutrition, but medical experts say it is only a matter of time before her deteriorating organs give out.

“This is basically organ support; it’s not life support,” said Dr. Neal E. Slatkin, a neurologist and chief medical officer at San Jose’s Hospice Of The Valley. “Her organs are alive, but she’s not alive. Her organs are slowly dying. Her fate is written; it’s just a question of when everything fails.”

Thursday marked one month since Jahi entered the Oakland facility on Dec. 9 for surgery to remove her tonsils and clear tissue from her nose and throat. Complications after surgery — massive bleeding, cardiac arrest and brain swelling — led doctors to declare her brain-dead Dec. 12, a diagnosis confirmed by multiple doctors.

After weeks of court battles, the family won the right to move her to another facility, and while they haven’t disclosed where she is being kept and who is caring for her, their attorney said this week that a new team of doctors are optimistic her condition has stabilized since she left Children’s Hospital on Sunday evening.

The new team of doctors has inserted a feeding tube and given the girl a tracheotomy to insert a breathing tube, but the family has refused to say where she is being treated. In a message sent Thursday, the family’s attorney, Christopher Dolan, would not offer specific information on Jahi’s condition.

“I am not the medical decision-maker,” Dolan said. “I had a singular role which was to help the mother be able to make the choice on her own as to whether or not the daughter would continue on a ventilator.”

However, the extent of her body’s deterioration was detailed in a court filing last week by Heidi R. Flori, a critical care pediatrician at Children’s Hospital. In the filing, Flori wrote that tissues under her skin were losing their elasticity, her muscles were contracting and blankets were needed to keep her at a constant temperature.

“This deterioration became inevitable the moment she died,” Flori wrote. “Additional and more dramatic signs of the body’s deterioration will continue to manifest over time, regardless of any procedures and regardless of any heroic measures that any facility might attempt.”

According to Slatkin, it is possible that the nutrients she is receiving are supporting her deteriorating organs, but he echoed comments from previous doctors who have said no medical tools or procedures can bring back someone who has been declared brain-dead.

“Dead is dead. There aren’t grades of dead,” Slatkin said. “Anything that (the attorney) or the family may perceive as improvement does not indicate that she is alive in any way.”

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